Should B'nai Noach get involved in politics?

Absolutely. In fact, the Noahide obligation to act against injustice, to establish, protect and maintain a system of just laws, police and courts, requires it. Put in negative terms, every human society is obligated to defend itself against anarchy, to replace the rule of the strong with the rule of justice - which can be achieved only through politics. Ultimately, politics is what authoritatively determines who gets what. Politics is a far better mechanism for deciding such issues than force or violence.

So we see that even the Biblical prophets involved themselves intensely in the political controversies of their times. Naturally: politics is where things happen! To refrain from political activity would be like refraining from life. Jeremiah, one of the greatest prophets, emphatically urged his people to concern themselves with civic affairs, even after they had been exiled from Israel, their homeland. His approach to politics is exemplified in this famous line, elucidating a basic Torah principle: "Seek the peace of the city whither I [that is, God] have caused you to be carried away captive, and pray unto the Lord for it: for in the peace thereof shall ye have peace." [Jeremiah 29:7]

In the United States today, many Noahides believe that the most important political issues that lie before society are abortion — which they generally oppose, capital punishment — which they generally support, keeping the reference to God in the Pledge of Allegiance, and opposing any legal validation of homosexual "marriage." These people tend to believe that the Republican party is stronger on all these issues - and also, generally, more opposed to sexual immorality and lewdness in the public sphere.

Some Noahides are passionate Democrats. These people tend to believe in protecting the powerful against the weak, being sensitive to environmental issues, and promoting fiscal responsibility. These issues are no less important than, say, enacting laws forbidding abortion.

In fact, God is neither Republican nor Democrat, neither "Green" nor "Libertarian," and no party has a monopoly on virtue or people of virtue.

Ultimately, each of us has to decide personally what issues are most important to us and where we stand on each one.

Regarding some of the issues mentioned above, it may be helpful to note that the Universal laws, the Law of the Rainbow Covenant, does NOT prohibit all abortion. In fact, the law makes abortion mandatory in certain circumstances, as when the life of the mother is endangered by the fetus, and the only way - literally - to save the mother's life is by destroying the fetus. In such circumstances, for instance, candidates proposing to ban so-called "partial birth abortions" (which aren't nearly as numerous, anyway, as people have been led to believe) are actually proposing to make compliance with God's law impossible.

Similarly, capital punishment is very problematic as a matter of Universal law - if only because true legal and moral guilt generally can't be established with the certainty required. A society that executes even one innocent person is a murderous society. Or, turning to the question of "gay marriage," while many Democrats earnestly oppose it, that doesn't mean that the best way to ban it is by legislating and enacting another new amendment to the U.S. Constitution.

Sexual immorality and public lewdness, the very opposite of sexual modesty, is pervasive in the Western world today. That doesn't mean that it will always be so. The idea, however, that one political candidate or another will be substantially "better" that way, by making substantial changes, is not realistic. That's not how change of that sort comes about. Virtue isn't something that we achieve by political fiat: it's something we have to work at. It normally comes from below, from the people, emerging from the currents of mainstream culture. Moses was unique in political history. In the world ever since, only a demagogue, a political opportunist, promises to make people virtuous by decree from above.